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Estimation, Learning and Parameters of Interest in a Multiple Outcome Selection Model

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  • Justin Tobias

Abstract

We describe estimation, learning, and prediction in a treatment-response model with two outcomes. The introduction of potential outcomes in this model introduces four cross-regime correlation parameters that are not contained in the likelihood for the observed data and thus are not identified. Despite this inescapable identification problem, we build upon the results of Koop and Poirier (1997) to describe how learning takes place about the four nonidentified correlations through the imposed positive definiteness of the covariance matrix. We then derive bivariate distributions associated with commonly estimated “treatment parameters” (including the Average Treatment Effect and effect of Treatment on the Treated), and use the learning that takes place about the nonidentified correlations to calculate these densities. We illustrate our points in several generated data experiments and apply our methods to estimate the joint impact of child labor on achievement scores in language and mathematics.

Suggested Citation

  • Justin Tobias, 2006. "Estimation, Learning and Parameters of Interest in a Multiple Outcome Selection Model," Econometric Reviews, Taylor & Francis Journals, vol. 25(1), pages 1-40.
  • Handle: RePEc:taf:emetrv:v:25:y:2006:i:1:p:1-40
    DOI: 10.1080/07474930500545421
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    Cited by:

    1. Djebbari, Habiba & Smith, Jeffrey, 2008. "Heterogeneous impacts in PROGRESA," Journal of Econometrics, Elsevier, vol. 145(1-2), pages 64-80, July.

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    Keywords

    Bayesian econometrics; Treatment effects;

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